William's Favorite Math Stuffs

Mathematicians:

• Euclid (325-270 BC) (Elements - the world's most definitive text on geometry)
  
• Isaac Newton (1642-1727) (most important contributor to the development of modern science, Newton's laws, calculus)
  
• Leonhard Euler (1707-1803) (most prolific mathematical writer of all time)
  
• George Polya (1887-1985) (heuristics in mathematical problem solving, Polya Enumeration Theorem)

Mathematical Theorems:

• Euler Formula
  
• Fundamental Theorem of Algebra
  
• Polya Enumeration Theorem
  
• Polyhedral formula
  
• Principle of Inclusion and Exclusion
  
• Pythagorean Theorem and its proof due to Euclid

Mathematical Books/URLs:

• Nathan Altshiler-Court, College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle, Dover Publications, Inc, New York, 2007.
• Euclid, The Elements, Books I-XIII, Barnes & Noble, 2006.
• Henry Sinclar Hall and Samuel Ratcliff Knight, Higher Algebra, Elibron Classics, 2005.
• G. Hardy, et al, Inequalities, 2nd Edition, Cambridge University Press, 1994.
  
• Stephen Hawking, God Created the Integers: The Mathematical Breakthroughs that Changed History, Running Press, 2005.
• Stephen Hawking, On the Shoulders of Giants: The Great Works of Physics and Astronomy, Running Press, 2002.
• James Newman, The World of Mathematics, Vol. 1-4, Dover Publications, Inc., New York, 1956.
• G. Polya, How to Solve It: A New Aspect of Mathematical Method, 2nd Edition, Princeton University Press, 1973.
• G. Polya, Mathematics and Plausible Reasoning, Vol. 1: Induction and Analogy in Mathematics, Princeton University Press, 1990.
• G. Polya, Mathematics and Plausible Reasoning, Vol. 2: Patterns of Plausible Inference, Princeton University Press, 1990.
• G. Polya, Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving, Combined Edition, Princeton University Press, 1981.
• G. Polya and Gabor Szego, Problems and Theorems in Analysis I and II, Springer-Verlag, 1988.
• John Riordan, Introduction to Combinatorial Analysis, Dover Publications, Inc., 2002.
• Art of Problem Solving
• Wolfram MathWorld

Mathematics Area:

• Number Theory and Analytic Number Theory
  
• Combinatorics and Graph Theory
  
• Game Theory
  
• Fuzzy Logic
  
• Postsecondary Mathematics Education

Quotes:

• A great discovery solves a great problem but there is a grain of discovery in the solution of any problem. Your problem may be modest, but if it brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery. -- George Polya*
  
• Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long as relations do not change. Matter is not important, only form interests them. -- Henri Poincare*
  
• The secret of science is to ask the right question, and it is the choice of problem more than anything else that marks the man of genius in the scientific world. -- Sir Henry Tizard*
  
• The intelligence is proved not by ease of learning, but by understanding what we learn. -- Joseph Whitney*
  
• The good Lord made us with two ends - one to sit on and one to think with. How well you succeed in life depends on which one you use. -- Isaac Dworetsky*
  
• The more you do, the more we can do. -- William Hazlitt*
  
• If you don't learn from your mistakes, there's no sense making them. -- Herbert V. Prochnow*
  
• The important thing in Science is not much to obtain new facts as to discover new ways of thinking about them. -- Sir William Lawrence Bragg*
  
• Superior intellect is a large development of the faculty of association by similarity. -- Alexander Bain*
  
• The thing that counts is not what we know but the ability to use what we know. -- Leo L. Spears*
• If I see further, it is because I stand on the shoulders of giants -- Isaac Newton

* Excerpts from Joseph A. Gallian, Contemporary Abstract Algebra, D. C. Heath and Company, 1986

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